Polar modes and isospectrality of Ellis-Bronnikov wormholes
Bahareh Azad, José Luis Blázquez-Salcedo, Xiao Yan Chew, Jutta Kunz, Dong-han Yeom
Abstract
We consider polar perturbations of static Ellis-Bronnikov wormholes and derive the coupled set of perturbation equations for the gravitational and the scalar field. For massless wormholes the perturbations decouple, and we obtain two identical master equations for the scalar and gravitational modes, which moreover agree with the master equation for the axial modes. Consequently there is isospectrality with threefold degenerate modes. For a finite mass of the background wormhole solutions, the equations are coupled. We then obtain two distinct branches of polar quasinormal modes for a given multipole number $l$, associated with the presence of the two types of fields. We calculate the quasinormal mode frequencies and decay rates for the branches with $l=2$, 3 and 4. For a given $l$ the real frequencies of the two branches get the closer, the higher the multipole number gets.